On node distributions for interpolation and spectral methods
Abstract
A scaled Chebyshev node distribution is studied in this paper. It is proved that the node distribution is optimal for interpolation in $C_M^{s+1}[1,1]$, the set of $(s+1)$time differentiable functions whose $(s+1)$th derivatives are bounded by a constant $M>0$. Node distributions for computing spectral differentiation matrices are proposed and studied. Numerical experiments show that the proposed node distributions yield results with higher accuracy than the most commonly used ChebyshevGaussLobatto node distribution.
 Publication:

arXiv eprints
 Pub Date:
 May 2013
 arXiv:
 arXiv:1305.6104
 Bibcode:
 2013arXiv1305.6104H
 Keywords:

 Mathematics  Numerical Analysis;
 65D05;
 41A05;
 41A10
 EPrint:
 18 pages, 8 figures